The interpretation of a large amount of data obtained for an interpretation space can be a very complex task. A particular example is the analysis of seismic and sometimes other data obtained for a subsurface formation, in order to allow discrimination among regions and layers of particular properties. The expression ‘subsurface formation’ is used herein to refer to a volume of the subsurface. A volume of the subsurface typically contains a plurality of layers. The subsurface formation can in particular include one or more layers containing or thought to contain hydrocarbons such as oil or natural gas, but it can also and even predominantly include other layers and geological structures.
Frequently, two or more data sets are available, each providing values of a distinct scalar parameter for different locations throughout the interpretation space. It is desired to interpret these data sets in conjunction so as to identify certain classes of regions in the interpretation space.
In the case of interpreting data obtained for a subsurface formation, so-called Amplitude Variations with Offset (AVO) technology is frequently applied. In the article “Successful AVO and Cross-Plotting” by S. Chopra, V. Alexeev and Y. Xu, GSEG Recorder, November 2003, p. 5-11, cross-plotting is discussed as a technique enabling simultaneous and meaningful evaluation of two attributes. In conventional cross-plotting, the values of two separate scalar parameters (attributes) belonging to a particular location in the interpretation space (in the subsurface formation) are plotted as a point in a separate two-dimensional space which can be referred to as attribute space. The two dimensions of the attribute space represent the two attributes considered.
In Example 1 of the Chopra article, the interpretation space is 1-dimensional along the trajectory of a wellbore through a subsurface formation. Along the wellbore, several well-log parameters (attributes) have been measured or derived from measurements, e.g. P-velocity Vp, S-velocity Vs, Rho, Mu, and Lambda (the Lamé parameters, representing respectively the bulk density, the shear modulus, and the compressional influence on the elastic moduli). 2-dimensional cross-plots of Vp vs. Vs, Lambda-Rho vs. Mu-Rho are presented, and also two cross-plots in which a three-dimensional attribute space was used. Geologic layers are identified along the wellbore, and in the cross-plot the points representing data from a specific type of geologic layer are plotted with a specific colour. In the cross-plot, clusters of points having mainly or exclusively the same colour can be seen. Conversely, by drawing a polygon around each of the clusters the operator can mark log zones along the well from which these data points originated.
A particular embodiment of the polygon method is discussed in a paper by P. Brenton and O. D. Duplantier “When Geology meets Geophysics—optimised Lithoseismic Facies Cubes for Reservoir Needs”, EAGE 68th Conference & Exhibition—Vienna, Austria, 12-15 Jun. 2006. In this paper, polygons drawn to separate facies groups in a cross-plot of log data are updated using petrophysical data. The occurrence probability of certain petrophysical parameters such porosity in certain facies or groups of facies is statistically analysed, and used to refine the facies group definition by polygon boundaries in the cross-plot. After the refined polygons have been determined, a 3D visualization of the result in interpretation space is done by the geologist.
There is a need for an improved interpretation method. In complex situations, such as when the distributions of the various classes are under-sampled or overlapping, and in particular when no or only few petrophysical data are available, the operator cannot confidently draw the polygons to distinguish among several classes of data. Also, when considering an attribute space with three or even more dimensions, the polygon method is insufficient.
It will be understood, that vector data can be considered as an assembly of scalar data, in particular scalar datasets for a corresponding plurality of locations. In particular, attribute vectors can always be considered to represent an assembly of co-located scalar datasets.